Electrooptic devices using the non-zero components of the second order polarizability tensor to achieve second harmonic generation, parametric amplification, the addition and subtraction of frequencies, tunable frequencies, modulation and the like of coherent electromagnetic radiation have been described by Albert A. Ballman, Gary D. Boyd and Robert C. Miller in U.S. Pat. No. 3,262,058, by J.A. Giordmaine and Robert C. Miller in U.S. Pat. No. 3,328,723, by Satoshi Nanamatsu and Masakazu Kimura in U.S. Pat. No. 3,747,022 by John Bierlein and Thurman Gier in U.S. Pat. No. 3,949,323 and by Chen Chuangtian, Wu Yicheng, Wu Bochang and You Guming in U.S. Pat. No. 4,826,283 which are incorporated herein in their entirety.
Electromagnetic waves propagating in a crystal having nonlinear optical properties induce polarization waves with frequencies that are the sum and the difference of the frequencies of the exciting waves. These polarization waves can radiate electromagnetic waves having the frequencies of the polarization waves. The energy transferred to a radiated electromagnetic wave from a polarization wave depends on the magnitude of the component of the second order polarizability tensor involved because this tensor element determines the amplitude of the polarization wave and also the distance over which the polarization wave and the radiated electromagnetic wave can remain sufficiently in phase, called the coherence length. The coherence length is give by ##EQU1## wherein .DELTA.K is the difference between the wave vector of the radiated electromagnetic wave and the wave vector of the polarization wave. Phase matching occurs when the waves are completely in phase, that is when .DELTA.K=0. The condition .DELTA.K=0 can also be expressed as n.sub.3 w.sub.3 =n.sub.1 w.sub.1 .+-.n.sub.2 w.sub.2 wherein w.sub.3 =w.sub.1 .+-.w.sub.2 and where w.sub.1 and w.sub.2 are the frequencies of the incident light and w.sub.3 is that of the radiated optical wave and the n's are the corresponding refractive indices. The plus signs are appropriate when the sum frequency is the one of interest; the minus signs are appropriate when the difference frequency is the one of interest. A particular case which will be used as a simple example of nonlinear effects in second harmonic generation (SHG) where there is only one incident wave of frequency w and w.sub.1 =w.sub.2 =w and w.sub.3 =2w.
The above phase matching conditions can be met with birefringent crystals provided the refractive index difference between the ordinary and the extraordinary rays is sufficiently large to offset the change of refractive index with frequency, i.e., optical dispersion.
A complication in this phase matching process is the fact that phase matching occurs only for certain crystallographic directions. If a light ray deviates from this phase-matched direction, a mismatch occurs and .DELTA.K is no longer zero. For example, when collinear phase-matched SHG is used such a situation occurs if the alignment of the incoming beam and the phase-matched crystallographic direction is not exact or if the incoming beam is slightly divergent. In general, .DELTA.K will be a linear function of the deviation .DELTA.e from the phase-matched direction. This places a restriction on the allowable angular divergence since a useful coherence length must be maintained. In addition, because of the double refraction, the radiated electromagnetic wave and the polarization wave will in general propagate in different directions, termed "walk-off", thereby reducing the interaction distance. Phase matching under these unfavorable conditions is called "critical phase matching" (CPM). For certain crystallographic directions, .DELTA.K does not vary linearly with the angular deviation .DELTA.e, but rather varies as (.DELTA.e).sup.2. As a result, greater divergence from the phase is allowable and no first-order "walk-off" occurs. Phase matching under these conditions is called "non-critical phase matching" (NCPM). The advantages of NCPM over CPM for practical devices are obvious. The indices of refraction can be adjusted by temperature variation or compositional variation in suitable cases so that phase matching occurs for crystallographic directions along which NCPM is possible. For biaxial crystals such as lithium triborate (LiB.sub.3 O.sub.5 or "LBO" crystals), NCPM conditions are possible for the SHG only when propagation is along certain of the principal axes of the optical indicatrix. (M.V. Hobden, J. Appl. Phys. 38, 4365 [1967])
The possibility of achieving one or more types of phase matching, and the appropriate orientation of the crystal to the incident wave depends on the existence of non-zero elements in the second order polarizability tensor. Depending on the point group symmetry of the crystal, some elements will be identically zero and equalities are imposed on other elements. The magnitude of the effects will depend on the magnitude of the non-zero elements.
Generally phase matching is one of two types:
Type I wherein the two incident waves have the same polarizations and
Type II wherein the two incident waves have orthogonal polarization.
Phase matching can be achieved by "tuning" the crystal in various ways.
(1) By rotation of the crystal to vary the refractive indices. PA1 (2) By varying the temperature. PA1 (3) By application of an electric field. PA1 (4) By compositional variation.
The preferred methods of tuning the crystal has been either to vary the temperature of the crystal or to rotate the crystal to vary the refractive indices. However, with extremely fragile crystals, such as LBO crystals, the temperature tuning method is not particularly suitable and may result in premature crystal failure. In addition, temperature tuning is slow, thereby limiting the stabilization bandwidth of the crystal. Accordingly, the preferred method of tuning LBO crystals is the crystal rotation method.
Prior to the present invention, nonlinear optical devices (NLO) have had fixed crystals set at the (presumably) optimal phase matching position. This arrangement precludes fine tuning of the crystal rotation to account for changes due to vibration, heat and other variables. As a result, most NLO's operate in a slightly out of phase condition, reducing the power output of the device.
In addition, prior to the present invention, the power output of the NLO was regulated by varying the intensity of the fundamental wavelength (.lambda..sub.1) emitted by the lasing medium by reducing the pumping of the power rod or, a polarization system can be used at the cavity output. Reducing the power rod pumping, however, modifies the thermal lens and creates instability. A polarization system only reduces the output power by a fixed amount and does not provide a means to adjust or optimize the power output.
Accordingly, a need has continued to exist for a method of optimizing and regulating the power output of a frequency doubled laser.